GROVE PRELIM 2U TEST YOURSELF 9 / GROVE PRELIM 3U TEST YOURSELF 10 - Q13

Multiply both sides by $x$.

$\displaystyle 2x=5+{3\over x}$

$\displaystyle 2x\times x=5\times x+{3\over x}\times x$

$$2x^2=5x+3$$

$$2x^2-5x-3=0$$

$$2x^2-6x+1x-3=0$$

$$2x(x-3) + 1(x-3)=0$$

$$(2x+1)(x-3)=0$$

$$\therefore x=-0.5, 3$$

JH2015 :-)

GROVE PRELIM 2U TEST YOURSELF 9 / GROVE PRELIM 3U TEST YOURSELF 10 - Q12

Here you use sum and product of roots formulas:

$\alpha+\beta = -b/a$ and 

$\alpha\beta=c/a$